SIMULATION OF SOLAR ENERGY GAIN THROUGH NATURAL LIGHTING SYSTEMS OF COMPLEX GEOMETRY

Natural lighting systems are important for the energy efficiency of the buildings. Thus the size of light openings should be optimized to provide visual comfort and decrease the energy needed to provide comfort in the environment. There exist tools to calculate solar energy gain in the buildings of mass construction with enclosing structures in the shape of horizontal and vertical planes. For structures with curvilinear surfaces systems of equations are compiled, to be solved by numerical methods with significant use of computer time. The article proposes a method of simulation solar energy gain for non-standard enclosing structures for buildings surrounded by existing housing using an apparatus of Balyuba–Naidysh point calculation (BN-calculus). Apparatus of BN-calculus allows forming of a point set optimized to match the shape of a geometrical object. Received point set is used to form elementary solid angles within which energy inflows from direct, scattered and reflected solar radiation into computational points are calculated. The sum of elementary values of energy inflows defines the total value of energy gain of the room.

Mkhitaryan, N. M. (1999). Energy from unconventional and renewable sources: experience and prospects. Kyiv: Naukova Dumka (in Russian).
Law of Ukraine. On the energy efficiency of buildings. 2118-VIII (2017). Retrieved from https://zakon.rada.gov.ua/laws/show/2118-19 (in Ukrainian).
Martynov, V.L. (2013). The rational orientation of windows in energy-efficient buildings. Energy-Efficiency in Civil Engineering and Architecture (Vol. 4, pp. 185–189). Kyiv: KNUCA (in Ukrainian).
Martynov V. L. (2013). Optimization of the orientation of energy-efficient buildings with compliance with the norms of illumination and insolation. Energy-Efficiency in Civil Engineering and Architecture (Vol. 5, pp. 84–89). Kyiv: KNUCA (in Ukrainian).
Sergeychuk, O., Avetikov, A., Lisovets V. (2001). Heat transfer through sloping windows in winter. Vitrina, 10, 16–23 (in Russian).
Sergeychuk, O. V. (2004). Some geometric problems of designing energy-efficient buildings. Collection of Scientific Works. Special Issue: Geometric And Computer Modeling: Energy Saving, Ecology, Design, 148–155. Kyiv: Vipol (in Russian).
Natural and artificial lighting, DBN V.2.5-28:2018. State Building Codes of Ukraine. (2018). Kyiv: Ukrarkhbudinform (in Ukrainian).
Energy performance of buildings. Method for calculation of energy use for heating, cooling, ventilation, lighting and hot water supply: DSTU B A.2.2-12:2015. National Standard of Ukraine. (2015). Kyiv: Ukrarkhbudinform (in Ukrainian)
Fanger, P. O. (1967). Calculation of thermal comfort: introduction of a basic comfort equation. ASHRAE Transactions 73(2): III.4.1.

Tabunshchikov, Yu. A. Brodach, M. M. (2002). Mathematical modelling and optimization of thermal efficiency of buildings. Moscow: AVOK-PRESS (in Russian).
Balyuba, I. G. & Naydysh, V.M. (2015). Point calculus: study guide. Melitopol: MSPU (in Russian).
Adonyev, E. O. (2017). Compositional geometric method. Melitopol: FOP Odnorog T.V. (in Ukrainian).
Naydysh, V. M. & Vereshchaga, V. M. (1994). Problems of numerical integration. Applied Geometry and Engineering Graphics. (Vol. 57, pp. 21–24). Kyiv: KSTUCA (in Russian).
Konopatsky, Ye. V. (2008). Geometric modelling of algebraic curves and their application in the design of surfaces in a dot calculus of Balyubi-Nidysha. (Doctoral dissertation). Melitopol (in Ukrainian).
Satellight. The European database of daylight and solar radiation. Retrieved from: http://www.satellight.com/core.htm (date: 04.02.2015).
Yehorchenkov, V. & Konopatsky, Ye. (2015). E. Principles of constructing light field model for a room with curvilinear quadrangular light openings by means of the dot calculation. Light & Engineering, 23(2), 43–48.
Bemporad, A. (1907). Versuch einer neun empirischen Formel zur Darstellung der Änderung der Intensität der Sonnenstrahlung mit der Zenitdistanz. Met. 3s., Bd. 24, H. 7, 306–313.
Wiener Ch. (1884). Lehrbuch der darstellenden Geometrie, T. 1, Leipzig.